Mathai-Quillen Formulation of Twisted N=4 Supersymmetric Gauge Theories in Four Dimensions

TL;DR

This paper explores three different topological twists of N=4 supersymmetric gauge theories in four dimensions using the Mathai-Quillen formalism, analyzing their moduli spaces and geometric properties.

Contribution

It provides a detailed mathematical formulation of three inequivalent twists of N=4 theories and connects them to topological invariants and monopole theories.

Findings

Identification of three inequivalent topological twists of N=4 theories

Analysis of moduli spaces and geometric features for each twist

Simplification of functional integrals in one of the topological theories

Abstract

We present a detailed description of the three inequivalent twists of N=4 supersymmetric gauge theories. The resulting topological quantum field theories are reobtained in the framework of the Mathai-Quillen formalism and the corresponding moduli spaces are analyzed. We study their geometric features in each case. In one of the twists we make contact with the theory of non-abelian monopoles in the adjoint representation of the gauge group. In another twist we obtain a topological quantum field theory which is orientation reversal invariant. For this theory we show how the functional integral contributions to the vacuum expectation values leading to topological invariants notably simplify.